(Special thanks to Jolt135 for many of the combos in this deck, Crandor for pointing out the rules loophole with Fork that keeps us from running it, and Gatherer for the images I'm leeching. Written by metroid composite. Original discussion here).

What's the highest, non-infinite-combo damage you can do on turn one?

The rules of this game are simple. You have a Vintage-legal deck. Your opponent has all Islands.dec. Your deck must not have a way to go infinite (sometimes these can be very subtle, so watch out!) You can assume all chance events go the way you want them to (perfect draw, win all your coinflips). You may not have more than 60 cards in your deck, and your sideboard has 0 cards (so no, you can't make your deck 74 cards by copying Burning Wish 14 times).

What's the most damage you can deal? This was the question we asked ourselves, and this article describes the outcome of our mad science.

Introduction -- Strategies

Imagine the following scenario: you have four Kiki-Jikis in the battlefield (thanks to Mirror Gallery), and you start tapping them targetting Doubling Season, which you can do thanks to Opalescence.

Kiki-Jiki #1

A token that's a copy of Doubling Season comes into the battlefield...but wait! When a token comes into the battlefield, Doubling Season says we put twice that many tokens instead. So...we have 3 Doubling Seasons in the battlefield.

Kiki-Jiki #2

We make a second token...but wait! Doubling Season #1 says twice that (2 tokens) Doubling Season #2 says twice that (4 tokens) and Doubling Season #3 says twice that (8 tokens). Now we have 11 Doubling Seasons in the battlefield.

Kiki-Jiki #3

We make 2*2*2*2*2*2*2*2*2*2*2 = 2^11 = 2048 copies of Doubling Season. Now we have 2059 Doubling Seasons in the battlefield.

Kiki-Jiki #4

We put 2^2059 copies of Doubling Season into play (that's a lot).

...and then we tap Serra's Sanctum for 66,185,228,434,044,942,951,864,067,458,396,061,614,989,522,267,577,311,297,802,947,435,570,493,724,401,440,549,267,868,490,798,926,773,634,494,383,968,047,143,923,956,857,140,205,406,402,740,536,087,446,083,831,052,036,848,232,439,995,904,404,992,798,007,514,718,326,043,410,570,379,830,870,463,780,085,260,619,444,417,205,199,197,123,751,210,704,970,352,727,833,755,425,876,102,776,028,267,313,405,809,429,548,880,554,782,040,765,277,562,828,362,884,238,325,465,448,520,348,307,574,943,345,990,309,941,642,666,926,723,379,729,598,185,834,735,054,732,500,415,409,883,868,361,423,159,913,770,812,218,772,711,901,772,249,553,153,402,287,759,789,517,121,744,336,755,350,465,901,655,205,184,917,370,974,202,405,586,941,211,065,395,540,765,567,663,193,297,173,367,254,230,313,612,244,182,941,999,500,402,388,195,450,053,080,385,548 mana.



And then we use Djinn Illuminatus to replicate Burst of Energy, untapping Kiki-Jiki 66,185,228,434,044,942,951,864,067,458,396,061,614,989,522,267,577,311,297,802,947,435,570,493,724,401,440,549,267,868,490,798,926,773,634,494,383,968,047,143,923,956,857,140,205,406,402,740,536,087,446,083,831,052,036,848,232,439,995,904,404,992,798,007,514,718,326,043,410,570,379,830,870,463,780,085,260,619,444,417,205,199,197,123,751,210,704,970,352,727,833,755,425,876,102,776,028,267,313,405,809,429,548,880,554,782,040,765,277,562,828,362,884,238,325,465,448,520,348,307,574,943,345,990,309,941,642,666,926,723,379,729,598,185,834,735,054,732,500,415,409,883,868,361,423,159,913,770,812,218,772,711,901,772,249,553,153,402,287,759,789,517,121,744,336,755,350,465,901,655,205,184,917,370,974,202,405,586,941,211,065,395,540,765,567,663,193,297,173,367,254,230,313,612,244,182,941,999,500,402,388,195,450,053,080,385,548 times (and every time Kiki-Jiki untaps, we're going to tap him again to copy more Doubling Seasons!)

Time-out for a moment, audience check: if you're grinning with glee right now, this article is probably for you, stick around and grab some popcorn. On the other hand if you're hissing, holding up garlic to the screen, and yelling 'the math, it burns!' trust me: it's only going to get worse. Get out now while you still can!

Tips and Strategies

There's a number of things to watch out for when trying to build on the combo; remember the maximum of 60 cards in the deck--you want to make sure that every card you add makes a real impact. For instance, if we used one Mana Reflection to boost Serra's Sanctum, it really wouldn't have that big of an effect. If we were to instead start with two Doubling Seasons in play, we'd do a fair bit better--it would go 2 -> 6 -> 70 -> 2^70 -> 2^(2^70), and then we tap for 2^(2^70). That'll boost the output of Serra's Sanctum by a lot more than a single mana reflection will (which makes it tap for twice 2^(2059), so 2^(2060)). Notice just how much smaller 2060 is than 2^70 = 1,180,591,620,717,411,303,424


But we can STILL do better than a second Doubling Season. If instead of that, we had a second Burst of Energy in our hand, well...that's going to be way WAY bigger in impact. We get to replicate Burst of Energy after Kiki-Jiki has untapped and copied Doubling Season bazillions of times.





Now is THAT the best we can do? Well...no, actually, it's not. What if we were able to return Burst of Energy over and over and over again from our graveyard by replicating oh, say, Fossil Find cast using Gaea's Cradle (and using Burst of Energy + replicate in between each Fossil Find copy). Then, instead of just casting and replicating Burst of Energy twice, we're doing it a bazillion times.


Layers are Everything -- Run Narrower Cards

You'll notice in the example above that adding an extra layer of repetition by adding in Fossil Find made a much, much bigger impact than trying to get more of the same effect. You'll notice also that it took the form of

'repeat this action until you run out of [resource]'.

In the case above, the first layer was the copies of Burst of Energy on the stack:

'Untap Kiki-Jiki and copy a Doubling season for each Burst of Energy on the stack'

The second layer was the number of Fossil Finds on the stack:

'Tap Serra's Sanctum and replicate Burst of Energy a LOT of times for each Fossil Find on the stack'

Now, note that some of our earlier builds were running cards like Mycosynth Lattice--this meant that instead of having six different kinds of mana (all five colours and colourless) we had a single kind of mana, and therefore fewer total resource pools. And with fewer resource pools we got fewer layers of recursion (i.e. we couldn't say 'do [task] until you run out of green mana').

Some terminology for layers

I'm going to be using Knuth's up arrow Notation. The idea of this is very simple:

5+5 = 5 + 1 + 1 + 1 + 1 + 1.

5*5 = 5 + 5 + 5 + 5 + 5.

5^5 = 5 * 5 * 5 * 5 * 5.

The philosophy behind Knuth's up arrow notation is 'why stop at three functions?'

5^^5 = 5^(5^(5^(5^5))).

5^^^5 = 5^^(5^^(5^^(5^^5))).

5^^^^5 = 5^^^(5^^^(5^^^(5^^^5))).

And so on. So, okay, let's remember our Doubling Season example above. Each time Kiki-Jiki copied Doubling Season, it counted X the previous number of Doubling Seasons, and adds 2^X more. Ignoring the adding part (which becomes insignificant pretty fast) it just does a 2^X increase. So if we do a copy with each of the four Kiki-Jikis, we get roughly 2^(2^(2^(2^2)))) = 2^^5. When we replicated Burst of energy 2^2059 times, what we got was something more-like 2^^( 2^2059 ). And then if we added in the replicated Fossil Find layer above all that, that means we're doing the 2^^() effect from Burst of Energy over and over, i.e. 2^^(2^^(2^^(2^^(...)))). Though hey, that looks familiar--in fact it looks rather like 2^^^(X). And then if we had some way to repeatedly bring back Fossil Find, we could up the ante again by doing 2^^^(2^^^(2^^^(...))), or roughly 2^^^^X.

Don't spend too much time worrying about what these numbers actually look like. Suffice it to say...

1. The numbers quickly get wayyyyyyy bigger than anything you could write in Scientific notation.
2. The only really important thing to watch is how many layers of recursion there are. Finding a way to spend two mana instead of three on a spell you're replicating quickly becomes barely-noticeable when the numbers are so large. Finding a way to cast your best spell a zillion times, however, is always a big deal (especially since you get a LOT more mana for the next replication after each casting).

Outline of current best deck

Okay, this article is going to take some time to write, so for the moment this is just an outline. Sorry for the places heavy on shorthand and short on humor.

Layer 0, the kickstart

Black Lotus, Channel, Eureka, Squee's Revenge, Channel the Suns

How it works

Opening Hand:
1. Black Lotus (GGG)
2. Channel (G left in pool)
3. Savannah (GG left in pool)
4. Channel the Suns (17 life, WURBGG left in pool)
5. Squee's Revenge (16 life, WBGG left in pool)

Remember, all luck is with us, not just a stacked deck, so we win all our coinflips and draw 50 cards. No need to count cards anymore!

Eureka (14 life, WB left in pool)

At this point, use Eureka to put all our permanents from our deck into the battlefield (Minion Reflector, Opalescence, March of the Machines, Nature's Revolt, Doubling Season, Kiki-Jiki, Rings of Brighthearth, Mana Reflection, Copy Enchantment (copying Doubling Season), Hammerheim, Savannah, Steward of Valeron, Llanowar Dead, Apprentice Wizard, Ęther Spellbomb, Mirror Gallery, Vedalken Orrery, Djinn Illuminatus, Holistic Wisdom).

We now have multiple Minion Reflector triggers, with Channel being the only way to pay for them. These are the ones to pay for:

Hammerheim (12 life) (not an option--need red sources since only our red spells can get us more red mana. Remember, the original Hammerheim will have summoning sickness, so if we don't copy it we can't produce red mana at all. However, copies of Hammerheim made with Minion Reflector will have haste).
Lucrezia (10 life) (Kiki-Jiki can't copy her, and we're out of blue mana)
Kiki-Jiki (8 life) (not strictly needed because he has haste, but he's awesome).

Kiki-Jiki should tap to copy Doubling Season (we already have two, so we get 2^2 = 4 copies). Or, actually we may as well pay 2 more life (6 life) to use Rings of Brighthearth to copy Kiki-Jiki's ability, getting us a total of 2 + 4 + 2^6 = 70 Doubling Seasons. Now resolve Kiki-Jiki's Minion Reflector trigger, putting 2^70 = 1,180,591,620,717,411,303,424 Kiki-Jikis into play. From here, we can use five Kiki-Jiki taps to get hasty versions of all of our mana producers and also Ęther Spellbomb (we can't bounce and replay Ęther Spellbomb itself if we don't have extra copies of Ęther Spellbomb). From here all the combo pieces are online, so follow the steps below.

Why these startup cards can't go infinite with any combo pieces

I'll focus on the cards used exclusively to get the combo started (Eureka, Channel, Black Lotus, Channel the Suns, Squee's Revenge).

* Channel: we have no source of life gain right now
* Eureka: With the number of permanents this deck has, it's a spell that adds maybe 100 mana. Once we get going we'll have spells that add much, much more mana than that.
* Channel the Suns: once again, we will have spells that add effectively much more mana (thanks to Mana Reflection)
* Black Lotus: It's a spell that adds 3 mana. As an artifact, it's a permanent that can't be copied. If March of the Machines is in play, it becomes an Artifact Creature, but does not trigger Minion Reflector because it dies as a state-based effect from being 0/0 before triggered abilities can go on the stack.
* Squee's Revenge: only 53 cards to draw in the deck (and it can only draw 52!)

Layers 1 and 2--what to do with UUUUUU

Doubling Season, Opalescence, Mana Reflection, Apprentice Wizard, Minion Reflector, Copy Enchantment, Ęther Spellbomb, March of the Machines

How it works

Bounce and replay Copy Enchantment copying Mana Reflection (UU used) and pay 2 with Minion Reflector; this will make a token come into the battlefield, and we'll get 2^X tokens, where X is the number of Doubling Seasons, which means our mana sources will tap for 2^(2^(X)) times what they'd normally tap for.

Tap one of your many Apprentice Wizard for 2^(2^(X))*3 (UUU used). Bounce (UUUU used) and replay Minion Reflector, paying the 2 to get a token (so that we get 2^X Minion Reflectors).

Bounce and replay Copy Enchantment, this time copying Doubling Season (UUUUUU), and pay 2 for EVERY Minion reflector you control costing us (2^X)*2 colourless mana (though remember we've got 2^(2^(X))*3 in our mana pool--we can afford it). Now we have 2^X Doubling Seasons tokens entering the battlefield one at a time. Each one will 2^X the number of Doubling Seasons, meaning the next token to enter the battlefield makes even more tokens, so we get... 2^(2^(2^(2^(...^(2^X)...)))), or roughly 2^^X.

Why it doesn't mess with layers above it

(Need to think more what I'm doing with these sections)

Layer 3 -- producing lots of blue mana

Princess Lucrezia, Vedalken Orrery

How it works

In combination with Mana Reflection, Princess Lucrezia will produce an amount of mana roughly equal to the number of Doubling Seasons you have. However, there's a bit of extra cleanup we need to do here. Apprentice Wizard should be bounced and replayed at some point (tap Lucrezia for mana, you get about 2^(2^X), then do one round of copying Doubling Season, you get 2^^(2^X), NOW is a good time to bounce and replay Apprentice Wizard because one Minion Reflector+Doubling Season will put many more hasty Wizards into the battlefield than we have blue mana left from tapping Lucrezia). You should also do the same thing with Ęther Spellbomb (using a spellbomb token to bounce and replay the original Spellbomb so that we don't run out).

One last trick, not strictly necessary, but you can pay all 2^^(2^X) Minion Reflector triggers on Mana Reflection, and then let them resolve one at a time, using Vedalken Orrery to do steps 1 and 2 at instant speed in between each Minion Reflection token coming into the battlefield. Just reduces the cost of each Doubling Season bounce cycle to UUUU instead of UUUUUU.

...Anyway, we're tapping Lucrezia for 2^(2^X) blue mana, and for every four blue mana we 2^^X the number of doubling seasons, so overall we're looking at 2^^(2^^(2^^(2^^...(2^^X)...))) which gives us 2^^^X.

Layer 4&5 -- What to do with one Black mana

I imagine some of you were wondering why we were running Princess Lucrezia. The answer is that she can't pay for her own mana cost, which stops her from going infinite by doing 'bounce, cast, tap for lots of mana, repeat'. Same with all the mana creatures in the deck (Apprentice Wizard is blue but can't produce blue; Lucrezia is black but can't produce black; Llanowar Dead is green but can't produce green; Steward of Valeron is white but can't produce white. And nobody produces red because Kiki-Jiki is hax).

Anyway when we're almost out of blue mana, we can spend ONE black mana to get a LOT of blue. Here's how: bounce Lucrezia, and replay her, paying for every single Minion Reflector trigger so that there are X triggers on the stack. Let one trigger resolve, putting X hasty copies of Lucrezia into the battlefield. Each time we tap a Lucrezia for blue mana, we make the Doubling Season and Mana Reflection count go from X to 2^^^X. So going through all the Lucrezias that just entered the battlefield will give us 2^^^(2^^^(2^^^(...^^^X...))) = 2^^^^X.

However, THAT was just a single Minion Reflector trigger. Now let a second trigger resolve, and we put 2^^^^X copies of Lucrezia into play. Repeat the above, then let another trigger resolve, and we put 2^^^^(2^^^^X) copies of Lucrezia into play. In total over all X triggers we effectively do 2^^^^^X.

Layer 6 -- producing lots of black mana

Llanowar Dead

How it works

Tap Llanowar Dead for X black mana, where X is roughly your number of Doubling Seasons. Now use all this mana to bounce and replay Lucrezia X times. We're repeatedly doing the operation 2^^^^^(), so that brings us to 2^^^^^^X.

Layer 7&8 -- What to do with one Green mana

We bounce and replay Llanowar Dead, doing the same trick as we did for Layer 4&5 above where we pay all X Minion Reflector triggers, then let them resolve one at a time. Each trigger resolution does 2^^^^^^^X. X trigger resolutions brings us up to 8 layers of recursion with 2^^^^^^^^X

Layer 9 -- producing lots of green mana

Steward of Valeron

How it works

Tap Steward of Valerion. Same deal as above, this brings us to 2^^^^^^^^^X.

Layer 10&11 -- What to do with one White mana mana

Bounce and replay Steward of Valeron. Same plan as above where each trigger resolving does 2^^^^^^^^^^X, and all X triggers resolving gives us 2^^^^^^^^^^^X.

Layer 12 -- producing lots of white mana

Savannah

How it works

Once again, mana reflection makes us tap for X white mana, resulting in a 2^^^^^^^^^^^^X effect. However, this is where things change. We CAN'T bounce and replay Savannah because of the one land per turn rule. (Unless we did a second casting of Eureka, but we're not quite ready to incorporate sorceries into this just yet).

Layer 13, 14, what to do with an untapped Kiki-Jiki

Kiki-Jiki, Rings of Brighthearth, Nature's Revolt

How it works

Bounce and replay Rings of Brighthearth so that the number of them in play is roughly equal to the number of Doubling Seasons, then tap Kiki-Jiki, and copy his ability X times using Rings of Brighthearth, all targetting Savannah (which is a creature thanks to Nature's Revolt). As always, we're going to let the triggers resolve one at a time, so that we can tap these Savannahs to make more Doubling Seasons before the next Savannah token comes into play. This brings us up to 2^^^^^^^^^^^^^^X.

Layer 15, 16, what to do with three Red mana (RRR)

As you might have guessed, we're going to bounce and replay Kiki-Jiki, and trigger all X copies of Minion Reflector, then put the tokens into play one at a time, only after the entire previous set of Kiki-Jikis is done massively upping our permanent count. Now we're up to 2^^^^^^^^^^^^^^^^X.

Layer 17 -- producing lots of red mana

Hammerheim

How it works

Once again we're using Mana Reflection here to get X red mana, which brings us up to 2^^^^^^^^^^^^^^^^^X. The important thing to note here, however is that Hammerheim is a legendary land, and therefore can NOT be copied by Kiki-Jiki (otherwise we would go infinite).

Layer 18, Heat Shimmer

Heat Shimmer (reusing Nature's Revolt to target Gaea's Cradle, and Doubling Season to put a lot of Gaea's Cradles into play)

How it works

Target Hammerheim with Heat Shimmer. Doubling Season means we put 2^X Hammerheims into play. Since Heat Shimmer does not have Kiki-Jiki's 'non-legendary' clause, this works just fine. Obviously tap each Hammerheim individually, bringing us up to 2^^^^^^^^^^^^^^^^^^X.

To note here--all higher levels of recursion will be spells, and not permanents that could be targetted with Heat Shimmer. This prevents going infinite using any of the combo pieces in-play.

Layer 19, Radiate

Radiate

How it works

Radiate copies Heat Shimmer for every permanent in play. In order for this to be a full layer of recursion, we need to target Hammerheim with Heat Shimmer roughly X times, where X is the number of permanents in play. One Radiate for 3RR doesn't do this, because most of the Heat Shimmer copies don't target Hammerheim. However, two Radiates for 6RRRR does do this (the first Radiate makes sure there's X Hammerheims in play, and the second Radiate makes X copies of Heat Shimmer to hit them all). Double the red mana requirement from RR to RRRR is really not a big deal at this point--I mean even with just exponents, the difference between (2^(2^100))/2 and (2^(2^100))/4 is...not much. It's 2^((2^100)-1) versus 2^((2^100)-2). Won't even show up in my approximation. Speaking of which, we're now at about 2^^^^^^^^^^^^^^^^^^^X.

Layer 20, Replicate

Djinn Illuminatus

How it works

When we cast Radiate, instead copy Radiate X times (targetting all of them at Heat Shimmer). This brings us to roughly 2^^^^^^^^^^^^^^^^^^^^X. Note of course that Djinn is a triggered effect for copying spells. We would not be able to get away with an activated ability that copied spells.

Note that replicate has largely removed any use for Storm in this deck. They both trigger off of casting a spell, and trigger at the same time. And for the curious--no multiple instances of replicate don't stack--replicate triggers off of paying additional costs at the time of casting.

Layer 21, Brining Radiate back.

Fossil Find

How it works

Play Fossil Find, replicating it as much as possible. Use each Fossil Find copy to return Radiate, if possible (I could invoke the 'perfect luck' clause, but whatever--if, say, five of our bazillion Fossil Finds happens to whiff...well the graveyard will be empty or one card from then on). Note that because Fossil Find doesn't target, it's not a problem that Radiate leaves the grave--no fizzling for us!

Now, due to the way the stack works, the replicate copies resolve first, and then the Fossil Find finally resolves, putting it in the graveyard. None of the copies nor the original spell can return the actual Fossil Find card, so we don't go infinite.

Everytime we replicate Fossil Find, we get X castings of Radiate. This puts us at about 2^^^^^^^^^^^^^^^^^^^^^X.

Layer 22, Holistic Wisdom

Holistic Wisdom

How it works

Copy Holistic Wisdom X times, where X the number of Rings of Brighthearth we have in play (for each copy, return Fossil Find). Surprisingly enough, this actually doesn't require redirection, even though it's targeted. The stack ends up looking like this (thanks Crandor!)


* copy of Holistic Wisdom's activated ability
* Rings of Brighthearth triggered ability
* Rings of Brighthearth triggered ability
* Rings of Brighthearth triggered ability
...
* Rings of Brighthearth triggered ability
* Rings of Brighthearth triggered ability
* Rings of Brighthearth triggered ability
* Holistic Wisdom's activated ability

So we can resolve one trigger each time Fossil Find hits the graveyard, and at the time we resolve the trigger we get to choose new targets for the copy. Hence the only copy that will fizzle to to a missing target is the original Holistic Wisdom activation.

Of course, being able to get X castings of Fossil Find means we get 2^^^^^^^^^^^^^^^^^^^^^^X.

Layer 23, Our Library

~30 random sorceries that don't let us go infinite, whose only real purpose is to be removed from the game by Holistic Wisdom.

How it works

Make sure we get all the cards from our library into our hand (Ęther Spellbomb can also draw cards!) Remember too that Eureka, Channel, Channel the Suns, and Squee's Revenge are sorceries which no longer serve any purpose--use four spare Fork replications to get those back into our hand. Now...see the instructions for Holistic Wisdom and do them roughly 30 times.

Okay, so this is the final layer, we can afford to be a bit more precise. We have 33 cards left in the deck. We have 4 additional sorceries that we opened with but no longer need. We're also not starting from 0 before the first card is removed to Holistic Wisdom. In particular, one replication of Fossil Find gets us about 2^^...(21 arrows)...^^( kinda large number ). This is larger than 2^^...(22)...^^( 2 ) = 4, and larger than 2^^...(22)...^^( 3 ) = 2^^...(21)...^^( 4 ). However, it's probably smaller than or close to 2^^...(22)...^^( 4 ) = 2^^...(21)...^^( 2^^...(21)...^^( 4 ) ). However, that number is exactly equal to 2^^...(23)...^^( 3 ), so it seems like that's our starting point before we remove a single card with Holistic Wisdom; hence we'll add 3 to our 37 sorceries we're removing.

Final result: about 2^^^^^^^^^^^^^^^^^^^^^^^40.

Swing FTW

Well that's the combo at the moment; nothing left to do but to swing with a lot of hasty Doubling Seasons. This is still a draft (I know the writing is bad in places). Stay tuned for updates.

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